Abstract

If P is a prime ideal in an integral extension domain A of a quasi-local domain R and if F is the quotient field of R, then the following results hold when R is integrally closed: height P = height P ∩ R; altitude A p = altitude A p ∩ F; ( A p )′ ∩ F = ( A p ∩ F)′, where the prime denotes integral closure. This paper is concerned with generalizing these results to the case where R is not integrally closed.

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